I am wondering about the best way to test the difference in means of a continuous outcome in LCA. I know that the est/se for each parameter estimate refers to test of the parameter being significantly different than zero. Would it be legitimate to use the following test statistic: For Example: (Mean in class 1)- (Mean in Class 2)/(SE in Class 2)

In the denominator you want to have the SE for the numerator and since the two terms in the numerator are correlated, you need to take into account their covariance (in line with correlated t test). You can get the needed info from TECH3. An easier way is to do this via chi-square testing using log likelihood differences between the model with means equal versus different.